410 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
accepting indirect rather than direct causal relations between 
instruments and included variables. (Such a compromise may 
result in different instruments for different equations when a 
limited-information estimator is used; this will be the case 
below). 
In the present section, we discuss the circumstances under 
which zero or low inconsistencies can be expected, leaving expli- 
cit use of the causal criterion to the next section. 
Now, two sets of candidates for treatment as instrumental 
variables are obviously present. The first of these consists of 
those variables which one is willing to assume truly exogenous 
to the entire system and the lagged values thereof; the second 
consists of the lagged endogenous variables. The dynamic and 
causal structure of the system may well provide a third set, 
however, and may cast light on the appropriateness of the 
use of lagged endogenous variables; to a discussion of this 
we now turn. 
5.2. The Theory of Block-Recursive Systems 
A generalization of the recursive systems already discussed 
is provided by what I have elsewhere termed « block-recursive 
systems » (*). In general, such systems have similar proper- 
ties to those of recursive systems when the model is thought 
of as subdivided into sets of current endogenous variables and 
corresponding equations (which we shall call sectors) rather 
than into single endogenous variables and their corresponding 
equations. 
Formally, we ask whether it is possible to partition the 
vectors of variables and of disturbances and the corresponding 
matrices (renumbering variables and equations, if necessary) 
to secure a system with certain properties. In such partition- 
(5) See Fisuer [8] 
61 Fisher - pag. 26